The aim of this paper is to compare the two analytical approximation techniques for calculating the mean first passage time for a Logistic-type tumor cell growth model with Gaussian colored noise.We respectively apply the method of singular perturbation analysis and the method based on small tau time approximation are adopted to obtain the mean first passage time escaping away from the stable equilibrium state to the unstable equilibrium state, and then the analytic results obtained from the two methods are compared with those obtained from Meant-Carlo simulations.The comparison illustrates that the singular perturbation method has a better accuracy than the method of small tau time approximation.